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Question

Suppose that y varies inversely with the square of x, and y=50 when x=4. Find y when x=5

Solution
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The statement " y varies inversely as x means that when x increases, y decreases by the same factor. In other words, the expression xy is constant:

xy=k

where k is the constant of variation.

Here, it is given that yvaries inversely with the square of x and y=50 when x=4, therefore,

x2y=k(4)2×50=kk=16×2500k=40000

Thus, the general equation is x2y=40000.

Since x=5, therefore,

x2y=40000(5)2y=4000025y=40000y=4000025=1600

Hence, y=1600 when x=5.

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